Electrical apparatus for simulating the time dependent response characteristic of neutronic reactors



MalCh 4, 1952 H. A. STRAUS ET AL. 2,587,919

ELECTRICAL APPARATUS FOR SNIULATING THE TIME DEPENDENT RESPONSE CHARACTERISTIC OF' NEUTRONIC REACTORS 5 Sheets-Sheet l Filed Nov. 28, 1949 l INVENTORS y ,4. zraus Henr' BYFo/*r' es H. Murray/:S

Pensa E. Be, Jr:

ATTAA/EY IIII I I I I I I I I I I I IIIwIIIIIIIIIIIII March 4, 1952 H. A. STRAUS ET A1. 2,587,919

ELECTRICAL APPARATUS FOR SIMULATING THE TIME DEPENDENT RESPONSE CHARACTERISTIC OF NEUTRONIC REACTORS Filed Nov. 28, 1949 3 Sheets-Sheet 2 u, u Q ankam-l &

+300v +300 v @a l @a V2 V3 (2l C3 300V 300 v FIZ RL? 300V el?,

Hm". w Q a @FH T1 U) j Q N INVENTOR5 Hen/jy A, Sfr-aas BY Forrest! h. Murr-ay Per-sa* P, Be, Jr:

ATTORNEY rFz. E.

March 4, 1952 H. A. STRAUS ET Al. 2,587,919

ELECTRICAL APPARATUS FOR SMULATING THE TIME DEPENDENT RESPONSE CHARACTERISTIC OF' NEUTRONIC REACTORS 4 TT'ORNEY Patented Mar. 4, 1952 ELECTRICAL APPARATUS FOR tSIMULTIN G THE TIME DEPENDENT RESPONSE CHAR- ACTERISTIC OF N EUTRONIG REACTORS Henry A. Straus, Baltimore, Md., and Persa R. Bell, Jr., and Forrest H. .Murray Oak Ridge, Tenn.. assignors `to the United States `,of Amer- Aicaas represented by the United 'States Atomic Energy v.Commission Application November 28, 1949, Serial No. 129,719

7 Claims. (Cl. 235-61) This'fnvention `relates generally tothe problem `.of controllingneutronic reactors, and more parity which vwill occur duringopera'tion as .a .result of the build up of iission products and the de pleton of fissionable material.

This. excess reactivity, whennot needed, of course, held or cancelled out by the insertion of control rods. Itis immediately `apparent/that y the presence of this Ilarge amount of excess reactivity .introduces the possibility of the .reactor powerlevelgetting completely out of control and rising exponentially with a period so small that the reactor may burn itself up before it can be shut down. Such a reactor must be controlled very.v carefully, and preferably automatically, to 'insure that `dangerous conditions do not occur.

:Theohject of the `present invention is to provide 'an `electrical device which has the same time-dependent `response Acharacteristic as a reaoto'11,that is, la device wherein anelectric `parameter. such as Ia voltage, varies with time Iin exactlyithe samemanner as does the neutron `diensityoareactor. Such'adevice has-innumerable usesjin connection with the design and `oper- -"a reactor. Among these uses are: (1) establishing proceduresfor start-up, shut-down, and operation of a reactor; '(2) training of manual operators in such procedure; `(3') ldesign and testing of l'servo systems and Aother components ,of ,automatic reactor control systems; (4) studies `of response of the .reactor to unusual `disturbances; and .(5) obtaining informationas to power levels which would .be attained should the reactor get ,out of control .of the normal control equipment and be eventually shut down 'by the emergency safety equipment.

In .the drawings:

Figure .111s a diagram showing the rates of occurrenceyof the various events which take place .in a lthermalneutron reactor .and `which 'lead to the production 'or` loss of neutrons from the re-f lactor. vIt is useful in explaining the dynamic rtheoryof.thermalneutron `reactors `and in debe made. ,gone into here, it leads to the `result that ``L2A riving the differential equations upon which the neutron reactor simulator of the present invention is based;

Figure 2 is a `wiring diagram of the reactor simulator of the present invention; and

Figure 3 is an internal `wiring diagram of the integrator ampliiier shown schematically in Figure 2.

Referring 'now to iFigure l, the large lower vrectangle illustrates any .representative 4portion of the reactor. The instantaneous number of thermal neutrons containedin .this representative portion at any time will be represented by the quantity n. The rectangle may be considered as the entire reactor, in which case n is the entire number of thermal neutrons present in thereactor, `or the rectangle :may be considered as an average cubic centimeter of the reactor, in Which case n is the average .neutron density within the reactor. In any case, the quantity n is proportional to the instantaneousifpower level `of the reactor and varies with time in the same manner as does the power level. The `average Avelocity of these thermal neutrons is represented by o and their -mean free path for absorption by M. Since the -total distance traversed per second by all oi' the n neutrons `is equal fto nv, and `since M 'is the average distance which must ybe trav- -ersed absorbed, then is the number of neutrons absorbed per second, that is, the thermal neutron absorption rate. The quantity yZ will `hereinafter be :used to `riesig-- nate lthe ratio This quantity l is the average lifetime as a thermal neutron of those neutrons which are absorbed. The thermal neutron ,absorption rate .is `then .als

In order to determine the rate of loss of neutrons as a result of leakage, a mathematical an'- alysis is `accordance with diffusion theory may Although such an analysis `will not be thermal neutrons leak from the reactorper thermal neutron absorbed, and that, of `those neutrons which are produced by ssion 'at iission energies, a fraction v(1-e"^) -is lost to thereactor by leakage during the process ol slowing 3 down to thermal energies. In the above expressions, L is the diffusion length for thermal neutrons (a measure of the net crow-flight distance a thermal neutron travels before. being absorbed) -r is the Fermi age (a measure of the square of the net crow-flight distance traveled by a neutron While being slowed doWn from fission to thermal energy) and A, a minus quantity referred to as the reactor Laplacian, is a measure of the poorness of the reactor geometry (size and shape) from the standpoint of leakage of neutrons out of the reactor. Since -LZA thermal neutrons leak from the reactor per thermal neutron absorbed, the thermal leakage rate is lost to the chain reaction in a non-fission v "absorption process.

In these expressions, 2a is the total macroscopic absorption cross section and g2; is the macroscopic absorption cross section for 'ssion. Accordingly, the flssion rate is equal to Elf ZE,

while the rate of loss of thermal neutrons by way of non-ssion absorption is equal to if' 2 g- Ef l E. n The average number of new neutrons ultimately 1 produced at the high iission energy as a result of is produced in potential form, that is, as iission-k a single fission will be represented by the quantity V. Of these ssion neutrons, a small fraction product delayed emitters each of which will even- .I tually emit a high energy delayed neutron. The K remaining fraction of ssion neutrons (1 is produced immediately as prompt neutrons. The rate of production of prompt fission neutrons then is given by the expression or substituting K for the quantity by the expression The rate of production of delayed emitters of all types is l* sumption that there is no leakage loss.

From the previously referred to results of the analysis of leakage loss during the slowing down Cru process, the rate of leakage loss of prompt neutrons during slowing down is equal to Therefore, the rate of production of thermal neutrons as a result of slowing down of prompt neutronsis equal to @lfm-mee It has previously been stated that a fraction ,8V of all neutrons which ultimately result from each fission is temporarily stored in the form of delayed emitters, the total delayed emitter production rate of all types being There are at least five different types or groups of such delayed emitters, each typehavng associated therewith a characteristic fraction i and a characteristic disintegration constant M. The quantity C1 represents the instantaneous number of delayed emitters of the ith type present within the reactor. Again, `as for the quantity n, o may be considered as the average delayed emitter density, rather than the total number of delayed emitters present the reactor, if desired. l

Although all of the delayed emitter types-'may be taken into consideration in the design ofthe reactor simulator, if desired, it was found Worthwhile from an accuracy standpoint to take into account only those four types having the smallest disintegration constants A (the longest half-life), the remaining types being treated as prompt neutrons. Accordingly, in the diagram only four Y delayed emitter groups are illustrated.

Considering in detail just the ith group 4of delayed emitters and their associated delayed neutrons as representative of all groups, the instantaneous rate of formation is equal to The instantaneous rate of production of delayed neutrons of this type is equal to Cile. Since it can be assumed to a close approximation that the delayed neutrons are emitted at fission energies, the instantaneous rate of leakage during slowing down is equal to Crm1-eV and the instantaneous rate of appearance of thermal neutrons after slowing down isequal to Cim-em.

It is apparent that ECI-)a represents the total instantaneous production rate of fast delayed neutrons from all types of emitters, and efAECl-M represents the total instantaneous rate of appearance of therm'aln'utrons as' a result of the slowing down `of "delayed'fast y' neutrons.

There may also be included within 'a 'reactor a non-fission source of neutrons IWhichqcontributes to the thermal neutrons present in thepile. Such a source is represented in the diagrarijof Figure 1 as accounting for a production rate of thermal neutrons equal to S. j

It should be stated that in the vforegoing analysis, two assumptions have been made: (1) that all neutron absorption takes place at thermal energies, and (.2) that the neutrons vare'slovved down from fissionto thermal energies in va time so small in comparison with 'theirV average-lifetime'as thermal neutrons l that it can bef-heglected. Both of these'assumptions are ver'yiclose :approximations to the true situation `for thermal 'reactors ias we are There concerned with.

,stantaneous -rate of vproduction and the instan- 4taneousrate of "loss1thereof,3 the following dif- 'ferential' equation may `-be written:

.Bearranging terms and simplifying, we obtain:

Equation .2 fcan .be placed in the following form:

Substituting the quantityfffor the parenthetical expression (K -e 'A +L2Ae the following basic equation is obtained: 4)

A is Acommonly referred to as the reactivity or exl,cess.reproduction factor vof the reactor. Physiecally, it ,is equal to .the ,increment in .the .number of thermal neutrons. `which ultimately results from the absorption of e"TA neutrons.` ema is the increment in the .number `of thermal neutrons which ultimately results from the absorption of :one neutron.. Disregardingfcfor the moment any non-fission source, itwillbe `apparent that when :thereactivity 'is equal to zero,the reactor is just critical, :and the upower `level will remain confstant `after suiiicient time has elapsed for the delayed :emitters -to have attained their' equilibrim concentrations. VIf the reactivity is positive, the power of the reactor ,must ultimately rise, and if the reactivity is negative, the power level must ultimately fall. n

-The .significance `of each of the terms on the right hand side of Equation 4 may fbe seen by reference to the diagram of Figure ,1. The first .term `would give directly-,if .there were-nonon-ssion :source S and.

"if fall Tfission neutrons were emitted as prompt ,.neutrons. In other words, the iirst'term `treats the :delayed neutrons .incorrectly .as prompt neutrons. This would lead ,to the correct result only when the :delayed emitters had attained their :equilibriumconcentration, that is, when the second land third terms were equal. The second and :third terms together correct Jfor the `error present in .the :first term when equilibrium con-- course, lconstitutes the production rate of thermal neutrons from any non-fission source which i may be present in the reactor.

Similarly, the instantaneous rate of changeof the number of delayed emitters of each type may be equated to the rate `oi production of such Vile-- layed `emitters lminus the ratelof `decay thereof, as follows:

Equations 4 and 5 are the basic equations upon which the theory and operation `of Athereactor simulator device are predicated.

The overall object of the device is to provide an output voltage which is at all times proportional to the neutronzdensityfml.. and '.theftime variations of which depend upon specific circuit parameters in thessame manner as the time variations of the reactor neutron density depend upon corresponding reactor parameters. Thus, in Fig. 2, there is provided on lead l a voltage which is positive with respect to ground by an amount proportional to the neutron density (n) and on lead 2 an equal negative polarityvoltage. A current is ythusread'on ammeter 3 which is proportional -to thelneutrondensity `(n) The pile parameter of main interest is the reactivity -since this y'is the `one `J`which willfbe l dei uberatelyvariedfto controithe piieidurmgeperation, as by moving control rods. This-pile 'parameter is represented in the instrument by the displacement of slider'4 'of variable resistance R9 from its Central position. The slider 4 thenmay be -`throught of as simulating the `pile control rod. `When the slider is 'in its exact lcentral position, equals zero and the pile )is just critical. Displacements of 'the slider above or 'below Vthe central `position correspond to proportional positive or negative'valus of d, respectively.

In considering the operation of the instrument, it will rst be assumed that the voltages on leads I and 2 are in :fact proportional to (-I-n) and (--n), respectively, `and that the Apotential of point P is fixed at `ground potential. 'Since fil Le v.and l `are both constants, it is apparent that the potentialof the slider 4 is proportional to the rst term of .Equation 4. The slider i4 is 'connected to theerid .of a cathode follower V9,.the amplification factor of which is substantially unity. The output of the `cathode follower V9, which 4appears as .th-,e cathode. potential, is applied across `R11. .,Accordingly, .the current through R11 is .also rproportional to .theflrst term of Equation 4, and ,maybe written:

(6) 4im1=C1-(1st. term of LEqu. f4)

the proportionality constant C; depending among otherthinss on .the value of R11.

` The current through Ri ais obviously :proportional to (-n) and since allthe vcoeiicientsof (n) :in the .second .term .of `Equation .4 are constants, this `current .is proportional to theisecond term of the equation. We 4may :thenwrite:

the proportionality constant Cz dep-ending upon Ris.

The four Asimilar resistance-capacitance series circuits linthe upper `portion of Fig. V2 `arefem- `ployed fto @obtain potentials proportional to' the number of y:delayed emitters Cirof each .of :the

four types considered inaccordance with the balance Equation V5 for the delayed .emittera The general equation for these series circuitsmay be written as follows:

wherein V is the potential at the upper terminal of the condensers and n, of course,`is Vthe potential of lead I.

The values of RI, R2, R3, R4, CI. C2, C3, and C4 are chosen such that Substituting l c f for RC in Equation 8 gives:

l dV

Multiplying Equation 9 by we obtain:

K- fcelr se] l lz ZX', dt LA, V n The general balance Equation 5 for the delayed emitters may be rewritten in a similar 'form as follows:

From a comparison of Equations 10 and 11,Y it is clear that the potential V which appears at `the upperA terminal of the respective condensers CI, lC2, C3, C4 is proportional in each case to the number of delayed emitters C1 of the corresponding delay group, the proportionality conm- I stant in `each case being equal to the quantity of summation represented by the third term of `:ltlvquation 4, the proportionality constant C3 depending among other things on RIZ. Similarly. the currents flowing through RI3, RI4, and RIS are proportional to the other elements,` respectively, of the summation term, the proportionality constant in each case being made equal to C3 by the proper choice ofresistance values Although we have assumed in the above that the output of the various cathode followers is *l proportional to their inputs, this is not strictly correct by reason of the bias required for the cathodeffoliower tubes. For instance, if we assume for the moment that the slider 4 is atvzero potential, then the potential of the cathode of Vcathode follower V9 will be perhaps a few volts The y positive to supply the proper grid bias. cathode follower output voltage is, therefore, equal to the summationof a voltage proportional to the input .-voltage, and a constant reference voltage. Accordingly, there will be an additional constant current flowing to point P through each of RII, RIZ, RI3, RI4, and R15 as a result of the constant reference voltages for the corresponding cathode followers. This current, which is measurable, we will call (const.)

:sol

ISO

It is apparent that another current (ifm) will ow to point P through RI'I, the value of which will depend only upon the position of slider 5 and the ohmic value of RII. The current (ian) can be lumped with the constant current (icona.) to obtain a total constant current which is proportional to the constant fourth term of Equation 4, which represents the external source. Thus, we obtain: M

13) o' ...metan #als The total current (it) flowing to point P, therefore, may be represented as follows:

(14) l 2 d t st. term n erm zt 'Ol(of Equ. l +02(of Equ. 1)+

3rd. term Y' 4th. term a of Equ. l)+c of Equ. l

The various circuit elements, which determine the proportionality constants, are Vchosen such that C1,=C2=C3=C4. Then,

@For (right-hand side of Equ. 4) :cud-n Point P is connected to the input of .an integrator amplifier which may be of the type described in P. -I. R. E., vol'. 35, pages M4-A52. As is there described, such an integrator is adapted to produce on its output lead 2 a potential which is at al1 times proportional to the negative of the time integral of the current flowing into its input. Thus, we may write for the voltage (E2) appearing on output lead 2:

Thus, we see that the potential of lead 2 is proportional to the negative of the neutron density, which justifies one of our original assumptions.

The actual integrator amplifier used is shown in Fig. 3. It differs from the one described infthe P.l I. R. E. reference in that a diiference amplifier is employed. Point P is connected to the grid of Aone side of a duo-triode V5, and point P', which is intermediate equal resistors RIS and R20, is

- connected to thegrid of the other side of the duotriode V5, both sides of the duo-triode having a large common unby-passed cathode resistance R34. The input voltage signal to the amplifier is the diierence between the potentials of points P and P', such a difference creating'an unbalance in the plate currents of the two halves of the duo-triode. Several additional stages V6, V1 and V8 of identical balanced amplification are employed so that a very large amplification factor is obtained for the amplifier as a whole. This balanced amplification arrangement increases the accuracy of the instrument and at the same time provides a convenient means of deriving a potential on output lead I which is equal and opposite to that on lead 2 and is, therefore, proportional to (n) as required. The negative output is fed back to point P through an integrating condenser C5. Also, a condenser Cl of the same capacity isconnected between. the: positive output lead l and groundl to provide symmetric loading ofthe output stage.

Since RI9 and R20 are equal, point P' is at ground potential. factor of the integrator amplifier is large (of the order of 10,000), the input to the amplifier is extremely small for even the maximum operating value of the output (n). Thereforepoint P also remains substantially fixed at ground potential, as originally assumed at the outset of, the. description.

This latterassumption maybe made absolutely correct by introducing a slight, inequality between,

RIS and R20. Thus, it can be seen that if RIS is made slightly greaterthan R20, point P will have a slightly negative potential. This inequality can be so proportioned that whatever the amplifier output value (n), the required input signal to produce 011,)1 will be just equal tothe amount that P' is below ground potential. Under such circumstances, point P will be exactly at ground potential, making our original assumption absolutely accurate and increasing the over-all accuracy of the instrument. It will be apparent that these circumstances can be maintainedonly so long as` the gain of the amplifier remains constant.`

The operation of the device has thus far been described on the basis of the (-l-n). and C-ni voltages on output leads I and 2 being equal and opposite and point` P` being at ground potential. These conditions are not required for satisfactory operation. If the output voltages on leads l and 2 are. not exactly equal, point P instead of being at ground potential will assume a new fixed reference potential midway between (-l-ni and (-41). The overall effect ismerely to shift the reference point of the instrument as a wholefrom ground to a potential midway between (el-n) and (-n).

The purpose of the cathodeV followers is to isolate the prior computing components. The prior components are only accurate in operating'as de-` scribed so long as they draw no current.` By introducing a cathode follower, we are able to provide an output which is proportional to the output of the prior computing component but f from which a current can be drawn.

Since many changes could be made in the above description and many widely different embodiments of this invention could be made without departing from the scope thereof, it is intended that all matter contained in the above description or shown in the accompanying drawings shall be interpreted as illustrative and not in a limiting sense.

We claim:

1. An electrical neutronic reactor simulator comprising a high gain integrator amplifier having an input signal and an output signal, said output signal being representative of the neutron density of a neutronic reactor, and means responsive to said amplifier output signal for generating said amplifier input signal, said lastnamed means including potentiometer means connected across said output signal for generating a first component signal proportional to the product of the neutron density and .the reactivity of said reactor, at least one series resistance-capacitance circuit connected to said output signal for generating a second component signal proportional to the density of delayed neutron emit- Also, since the amplification fifi ters of a given type, means also connected to said output signal for generating a third: component signal proportional to the` neutron density and having a polarity opposite to that of said second component signal, and means for additively combining said three componentsignals to obtain said amplifier input signal.

2. An electrical neutronic reactor simulator comprising a high gain integrator amplifier having an input signal and an output signal, said output signal being representative of the neutron.

density of a neutronic reactor, means responsive to said amplifier output signal: for generating said amplifier input signal, said last-named meansincluding potentiometer means connected across said output signal` for generating a rst component signal proportional to the product of the neutron density andthe reactivity of said reactor,` at least one series resistance-capacitancel circuit connected to said output signal for generating aL second component signal proportional to the density of delayed neutron emitters of aV given type, means also connected to said outputsignal for generating a` third component signal,v proportional to the neutron density and having a polarity opposite to that of saidsecond component signal, means for generating a fourth manually controllable component signalindependent of said output signal, and means for additively combining said four component signals,v to obtain said amplifier. input signal.

3. An electrical neutronic reactor simulator comprising an integrator amplifier; said integrator amplifier including a difference amplifier train adapted to produce at its output terminalstwo equal and opposite voltages, and an integrating condenser connected between the positive side of the amplifier input and the negative side of the amplifier output; at least one series resistance-capacitance circuit connected between the positive side of the amplifier outputland ground; a voltage divider connected between the opposite sides ofthe amplifier output, said voltage divider having a manually controllable slider; a resistor connected between the negative side of the; amplier output and the positive` side of the amplifier input; and means connecting the condenser of said resistance-capacitance circuit and the slider of said voltage divider to the positive side of the amplifier input.

4. An electrical neutronic reactor simulator comprising an integrator amplifier; said integrator amplifier including a difference amplifier` train adapted to produce at its output terminals two equal and opposite voltages, and an integrating condenser connected between the positive side of the amplifier input and the negative side ofthe amplifier output; 'a plurality of circuits, each of which comprises a series resistance-capacitance circuit connected between the positive side of the amplifier output and ground, and a cathode follower the grid of which is connected to the ungrounded side of the condenser of said series circuit and the cathode of which is connected through a resistive network to the positive side of the amplifier input; a voltage divider connected between the opposite sides of the amplifier output, said voltage divider having a manually controllable slider; another cathode follower the grid of which is connected to the `slider of said divider and the cathode of which is connected through a resistance to the positive side of the ampliiier input; and a resistor connected between the negative side of the amplifier output and the T5 positive side of the amplifier input.

5. An electrical neutronic reactor simulator comprising an integrator amplifier; said integrator amplifier including a difference amplifier train adapted to produce atits output terminals two equal and opposite voltages, and an integrating condenser connected between the positive side of the amplifier input and the negative side of the amplifier output; a first resistor connected between the positive side of the amplifieroutput and the negative side of the amplifier input; a second slightly smaller resistor connected between the negative side of the amplifier output and the negative side of the ampliiier input; a plurality of circuits, each of which comprises a series resistance-capacitance circuit connected between the positive side of the amplifier output and ground, and a cathode follower the grid of which is connected to the ungrounded side of the capacitance of said series circuit and the cathode of which is connected through a resistive network to the positive side of the amplifier input; a voltage divider connected between the opposite sides of the amplifier output, said voltage divider having a manually controllable slider; another cathode follower the grid of which is connected to the slider of said divider and the cathode of Y which is connected through a resistance to the positive side of the amplifier input; a resistor connected between the negative side of the amplifier output and the positive side of the amplifier input; means for` providing a manually controllable source of positive potential; a resistance connected between said source and the positive side of the amplifier input; and means for visually indicating the magnitude of the amplifier output.

6. An electrical neutronic reactor simulator comprising an integrator amplifier; said integrator amplier including a difference amplifier train adapted to produce at its output terminals two ,equal and opposite voltages, and an integrating condenser connected between the positive side of the amplifier input'and the negative side of the amplifier output; a voltage divider connected between the opposite sides of the amplifier output; said voltage divider having a manually l2 controllable slider, and means connecting the slider of said voltage divider to the positive side of the amplifier input. Y

7. An electrical neutronic reactor simulator comprising an integrator amplifier; said integrator amplifier `including a difference amplifier train adapted to produce at its output terminals two equal and opposite voltages, and an integrating condenser connected between the positive side of the amplifier input and the negative side of the amplifier output; a voltage dividerconnected between the opposite sides of the amplifier output, said voltage divider having a manually controllable slider; and a cathode follower the grid of which is connected to the slider of said divider and the cathode of which is connected to the positive side of the amplifier input.r f

HENRY A. STRAUS. PERSA R. BELL, JR. FORREST H.` MURRAY.

REFERENCES CITED The following references are of record ln the file of this patent:

Principles of Radar, M. I. T. Radar School Staff, Chapter 2, p. 8, McGraw-Hill Book Co.; 1946.

Electrical Analogy Methods Applied to Servo` Methods of Computation; G. D. McCann et al.;

Proceedings of the I. R. E.; vol. 37, No. 8; pages 954-961; August 1949. 

